Could have to do with the timing/rhythm of the rope and physical movement.
And yeah, the rope getting snagged is a real bitch.
Usually happens when I get winded.
And keeps happening until I toss the damn thing and take my rage out on chocolate cake.

When you're jumping rope, try to isolate the motion to your wrists and ankles. A lot of beginners want to jump using the knees and hips, and that doesn't really work with the speed you need to keep the rhythm of a jump rope. Clear the rope as you jump, but recognize that you really don't need to jump very high.